the Thermodynamic Scale of Temperature. 303 
may be written 
Divide by t 2 and we have 
1 fdv\ v_ _ JK \v 
t\dtL f~ 
t* 
Suppose that the suffixes 1 and applied to v and t refer 
to the boiling and freezing points respectively ; then let us 
integrate the last equation with regard to t from t to t x 
at constant pressure p ; we shall obtain 
^"^ = X I^-^ = Xl(Say) - 
Multiply bv ' and transpose ; we obtain 
- = r + - **• 
Similarly by integrating at constant pressure />' we may 
obtain 
where dashed letters refer to the pressure j/. Subtracting 
and dividing by t l — t , we have 
where a denotes the coefficient of expansion at constant 
pressure. Hence 
If we calculate X from this formula we shall be able to 
turn the numbers found by Joule and Kelvin into absolute 
values. We notice that a small percentage error in the value 
of A will involve only the same percentage error in the fmally 
accepted values for the Joule-Thomson effect, — itself a small 
quantity. Hence it is permissible to employ approximate 
methods to some extent in calculating X. Thus we see that 
we require to know the values of t and t } : if we employ 
values for these quantities obtained from an uncorrected 
Y2 
